Call Now to Set Up Tutoring:

(888) 888-0446

SAT II Math I : Sequences

Study concepts, example questions & explanations for SAT II Math I

Create An Account

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Sequences

The first two numbers of a sequence are, in order, 1 and 4. Each successive element is formed by adding the previous two. What is the sum of the first six elements of the sequence?

Possible Answers:

Correct answer:

Explanation:

The first six elements are as follows:

$a_{1} = 1 \;$

$a_{2}= 4$

$a_{3} = 1 + 4 = 5$

$a_{4} = 4 + 5 = 9$

$a_{5} = 5+ 9 = 14$

$a_{6} = 9 + 14 = 23$

Add them:

1 + 4 + 5 + 9 + 14 + 23 = 56

Report an Error

Example Question #1 : Sequences

The first and third terms of a geometric sequence are 3 and 108, respectively. All What is the sixth term?

Possible Answers:

Insufficient information is given to answer the question.

$-265\frac{1}{2}$

-23,328

23,328

$265\frac{1}{2}$

Correct answer:

Insufficient information is given to answer the question.

Explanation:

Let the common ratio of the sequence be . Then The first three terms of the sequence are $3,3r,3r^{2}$ . The third term is 108, so

$3r^{2} =108$

$r^{2} = 36$

r = 6 or r = -6 .

The common ratio can be either - not enough information exists for us to determine which.

The sixth term is

$a_{1}r^{6-1} = 3r^{5}$

If r = 6 , the seventh term is $3 \cdot 6^{5}= 3 \cdot 7,776 = 23,328$ .

If r =- 6 , the seventh term is $3 \cdot \left (-6 \right )^{5}= 3 \cdot \left (-7,776 \right )= -23,328$ .

Therefore, not enough information exists to determine the sixth term of the sequence.

Report an Error

Example Question #1 : Sequences

The first and third terms of a geometric sequence are 2 and 50, respectively. What is the seventh term?

Possible Answers:

Insufficient information is given to answer the question.

146

31,250

-31,250

Correct answer:

31,250

Explanation:

Let the common ratio of the sequence be . Then The first three terms of the sequence are $2,2r,2r^{2}$ . The third term is 50, so

$2r^{2} = 50$

$r^{2} = 25$

r = 5 or r = -5 .

Not enough information is given to choose which one is the common ratio. But the seventh term is

$a_{1}r^{7-1} = 2r^{6}$

If r = 5 , the seventh term is $2 \cdot 5^{6}= 2 \cdot 15,625 = 31,250$ .

If r = - 5 , the seventh term is $2 \cdot\left ( -5 \right )^{6}= 2 \cdot 15,625 = 31,250$ .

Either way, the seventh term is 31,250.

Report an Error

Example Question #2 : Sequences

The sum of 3 odd consecutive numbers is 345. What is the largest number in the sequence?

Possible Answers:

121

117

119

103

Correct answer:

117

Explanation:

When you are dealing with arithmetic means, it is best to define one number in the sequence as x and every other number relative to x.

Because we are trying to find the largest of three numbers, let's define x as the largest number in the equation. Because each number is a consecutive odd number, we must subtract 2 to get to the next number in the sequence.

x: largest number in sequence

x-2: middle number in sequence

x-4: smallest number in sequence

Now, let's make an equation finds the sum of all the numbers in the sequence and set it equal to 354.

$\small x+(x-2)+(x-4)=345$

$\small 3x-6+6=345+6$

$\small \frac{3x}{3}=\frac{351}{3}$

$\small x=117$

117 is the largest number in the sequence.

To check yourself, you can add up the numbers in the sequence {113, 115, 117}.

$\small 113+115+117=345$

Report an Error

Example Question #5 : Sequences

2, 6, 3, 9, 4.5, ?

What is the next number in the sequence?

Possible Answers:

2.25

13.5

Correct answer:

13.5

Explanation:

The first number is multiplied by three

$\left ( 2*3=6 \right )$ .

Then it is divide by two

$\left (6/2=3 \right )$ .

The following is multiplied by three

$\left ( 3*3=9\right )$

then divided by two

$\left ( 9/2=4.5\right )$ .

That makes the next step to multiply by three which gives us

4.5*3=13.5 .

Report an Error

Example Question #62 : Mathematical Relationships

An arithmetic sequence begins as follows:

$0.3, \frac{1}{3} ,...$

Give the tenth term of this sequence.

Possible Answers:

$\frac{3}{5}$

$\frac{11}{15}$

$\frac{7}{10}$

$\frac{2}{3}$

$\frac{19}{30}$

Correct answer:

$\frac{3}{5}$

Explanation:

Rewrite the first term in fraction form: $0.3 = \frac{3}{10}$ .

The sequence now begins

$\frac{3}{10}, \frac{1}{3}$ ,...

Rewrite the terms with their least common denominator, which is LCM (3, 10) = 30 :

$\frac{3}{10} = \frac{9}{30}$

$\frac{1}{3} = \frac{10}{30}$

The common difference of the sequence is the difference of the second and first terms, which is

$d = \frac{10}{30} - \frac{9}{30} = \frac{1}{30}$ .

The rule for term $a_{n}$ of an arithmetic sequence, given first term $a _{1}$ and common difference , is

$a_{n} = a_{1} + (n-1)d$ ;

Setting $a_{1}= \frac{3}{10}$ , n = 10 , and $d = \frac{1}{30}$ , we can find the tenth term $a_{10}$ by evaluating the expression:

$a_{10} = \frac{3}{10} + (10-1) \frac{1}{30 }$

$= \frac{3}{10} + 9 \cdot \frac{1}{30 }$

$= \frac{3}{10} + \frac{9}{30 }$

$= \frac{9}{30} + \frac{9}{30 }$

$= \frac{18}{30 }$

$= \frac{3}{5}$ ,

the correct response.

Report an Error

Example Question #6 : Sequences

A geometric sequence begins as follows:

$\sqrt{20} , \sqrt{180},...$

Express the next term of the sequence in simplest radical form.

Possible Answers:

$17 \sqrt{5}$

$10 \sqrt{5}$

$18 \sqrt{5}$

Correct answer:

$18 \sqrt{5}$

Explanation:

Using the Product of Radicals principle, we can simplify the first two terms of the sequence as follows:

$a_{1}=\sqrt{20} = \sqrt{4} \cdot \sqrt{5} = 2 \sqrt{5}$

$a_{2}= \sqrt{180} = \sqrt{36} \cdot \sqrt{5} = 6 \sqrt{5}$

The common ratio of a geometric sequence is the quotient of the second term and the first:

$r = \frac{a_{2}}{a_{1}}= \frac{6 \sqrt{5}}{2\sqrt{5} } = 3$

Multiply the second term by the common ratio to obtain the third term:

$a_{3} = r a_{2} = 3 \cdot 6 \sqrt{5} = 18 \sqrt{5}$

Report an Error

Example Question #64 : Mathematical Relationships

The second and third terms of a geometric sequence are 3 i and , respectively. Give the first term.

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

Correct answer:

$-\frac{3}{2}$

Explanation:

The common ratio of a geometric sequence is the quotient of the third term and the second:

$r =\frac{a_{3} }{a_{2}} = \frac{-6}{3i} = \frac{-2}{i}$

Multiplying numerator and denominator by , this becomes

$r = \frac{-2}{i} = \frac{-2(-i)}{i (-i)} = \frac{-2i}{ -i^{2}} = \frac{-2i}{ -(-1 )} = \frac{-2i}{1} = -2i$

The second term of the sequence is equal to the first term multiplied by the common ratio:

$r \cdot a_{1} = a_{2}$ .

so equivalently:

$a_{1} =\frac{ a_{2}}{r}$

Substituting:

$a_{1} =\frac{ 3i}{-2i} = -\frac{3}{2}$ ,

the correct response.

Report an Error

Example Question #1 : Sequences

A geometric sequence begins as follows:

4 i , 1 ,...

Give the next term of the sequence.

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

None of the other choices gives the correct response.

$-\frac{1}{4} i$

$\frac{1}{4} i$

Correct answer:

$-\frac{1}{4} i$

Explanation:

The common ratio of a geometric sequence is the quotient of the second term and the first:

$r = \frac{a_{2}}{a_{1}}= \frac{1}{4i}$

Simplify this common ratio by multiplying both numerator and denominator by :

$r = \frac{1}{4i} = \frac{1 \cdot i}{4i \cdot i } = \frac{i}{4 i^{2}} = \frac{i}{4 (-1)} = \frac{i}{-4 } = -\frac{1}{4} i$

Multiply the second term by the common ratio to obtain the third term:

$a_{3} = r a_{2} = -\frac{1}{4} i \cdot 1 = -\frac{1}{4} i$

Report an Error

Example Question #66 : Mathematical Relationships

A geometric sequence has as its first and third terms and 24, respectively. Which of the following could be its second term?

Possible Answers:

None of these

$-18 \sqrt{2}$

$-18 i \sqrt{2}$

$-12 \sqrt{2}$

$-12 i \sqrt{2}$

Correct answer:

$-12 i \sqrt{2}$

Explanation:

Let be the common ratio of the geometric sequence. Then

$a_{2} = r a_{1}$

and

$a_{3} = r a_{2}= r \cdot r a_{1} = r ^{2}a_{1}$

Therefore,

$r ^{2} = \frac{a_{3}}{a_{1}}$ ,

and

$r = \pm \sqrt{ \frac{a_{3}}{a_{1}}}$

Setting $a_{1}= -12, a_{3} = 24$ :

$r = \pm \sqrt{ \frac{24}{-12} } = \pm\sqrt{-2} = \pm \sqrt{-1} \cdot \sqrt{2} = \pm i \sqrt{2}$ .

Substituting for and $a_{1}$ , either

$a_{2} = r a_{1} = \pm i \sqrt{2} \cdot (-12) = \mp 12 i \sqrt{2}$ .

The second term can be either $-12 i \sqrt{2}$ or $12 i \sqrt{2}$ , the former of which is a choice.

Report an Error

View SAT Subject Test in Mathematics Level 1 Tutors

Edem
Certified Tutor

University of Ghana, Bachelor, Mathematics. African Institute of Mathematical Science, Master's/Graduate, Mathematics.

View SAT Subject Test in Mathematics Level 1 Tutors

Lawrence
Certified Tutor

Imperial College England, Bachelor of Engineering, Mechanical Engineering. Columbia University in the City of New York, Docto...

View SAT Subject Test in Mathematics Level 1 Tutors

Rodolfo
Certified Tutor

The University of Texas at San Antonio, Bachelor of Science, Mathematics.

All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Dallas Fort Worth, ISEE Tutors in San Diego, Algebra Tutors in Phoenix, Chemistry Tutors in Miami, LSAT Tutors in Atlanta, Physics Tutors in Washington DC, MCAT Tutors in Denver, English Tutors in Dallas Fort Worth, GRE Tutors in Dallas Fort Worth, LSAT Tutors in Chicago

Popular Courses & Classes

SAT Courses & Classes in Chicago, GRE Courses & Classes in Dallas Fort Worth, ACT Courses & Classes in Washington DC, SAT Courses & Classes in New York City, LSAT Courses & Classes in Denver, MCAT Courses & Classes in New York City, MCAT Courses & Classes in Houston, GMAT Courses & Classes in Denver, GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Seattle

Popular Test Prep

GMAT Test Prep in Chicago, GRE Test Prep in Dallas Fort Worth, ISEE Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Los Angeles, ACT Test Prep in Washington DC, SAT Test Prep in San Diego, ISEE Test Prep in San Francisco-Bay Area, GMAT Test Prep in Dallas Fort Worth, SAT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

SAT II Math I : Sequences

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Sequences

Example Question #1 : Sequences

Example Question #1 : Sequences

Example Question #2 : Sequences

The sum of 3 odd consecutive numbers is 345. What is the largest number in the sequence?

117 is the largest number in the sequence.

Example Question #5 : Sequences

Example Question #62 : Mathematical Relationships

Example Question #6 : Sequences

Example Question #64 : Mathematical Relationships

Example Question #1 : Sequences

Example Question #66 : Mathematical Relationships

All SAT II Math I Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: